Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

A “guesstimate” is a “guess/estimate.” Business and government economic forecasting involves what many call “guesstimates” or “guesstimation.”

The word “guesstimate” is cited in print since at least 1904. The 1928 New York (NY) Times credited A. N. Gitterman for introducing a “new word,” but the word was not new in 1928.

“Guestimate” has been cited since 1905, but this spelling is used less frequently (perhaps from the similarity to “guest” rather than “guess").

Wikipedia: GuesstimateGuesstimate is a portmanteau of the words guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture. Like the word estimate, guesstimate may be used as a verb or a noun (with the same change in pronunciation).

The word is sometimes classified as informal English. It may be used in a pejorative sense or as an informal synonym for “estimate”.

Guesstimation techniques are used:

. in physics, where the use of guesstimation techniques to solve Fermi problems is taught as a useful skill to science students.
. in cosmology, where the Drake equation is a well-known guesstimation method.
. in economics, where some economic forecasts and statistics are based on guesstimates.

Lawrence Weinstein and John Adam’s book Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin, based on the course “Physics on the Back of an Envelope” at Old Dominion University, promotes guesstimation techniques as a useful life skill.

The Free Dictionary
Noun
1. guestimate - an estimate that combines reasoning with guessing
guesstimate
approximation, estimate, estimation, idea - an approximate calculation of quantity or degree or worth; “an estimate of what it would cost”; “a rough idea how long it would take”

(Oxford English Dictionary)
guesstimate, n.
orig. U.S.
[f. GUESS n. + ES)TIMATE n.]
An estimate which is based on both guesswork and reasoning.
1936 N.Y. Times 22 Dec., ‘Guesstimates’ is the word frequently used by the statisticians and population experts.
1943 N.Y. Times 19 July 4/6 Many Americans..think the Axis..will be defeated in less than two years. Intangibles..might make this popular ‘guestimate’ close to correct.
1948 Jrnl. R. Aeronaut. Soc. LII. 614/2 The former is a firm figure which arises in fact. The latter is an arbitrary ‘guesstimate’.
1957 R. WATSON-WATT Three Steps to Victory liii. 316 This mixture of estimates and guestimates comes out better than we deserve, for the Opana clock was very unlikely to agree with whatever clocks and watches were consulted in the aircraft and in Pearl Harbor.

19 November 1912, Fort Wayne (IN) Journal-Gazette, pg. 14, col. 3:
An early estimate of 45,000 hogs was posted, which was in excess of the estimate, but late trains did not come hoggy and the guesstimate was cut to 40,000 or less.

6 May 1928, New York (NY) Times, pg. 197:
“GUESSTIMATE” APPRAISAL.
Realtor Coins New Word to Express
Careless Methods.
A. N. Gitterman, who was a speaker at the meeting of the Long Island Real Estate Board last week, introduced a new word in the vocabulary of appraisers—“guesstimate” which he defined as “an expression of an estimate that is arrived at by guesswork without accuracy, without knowledge of detail or a full consideration of records” and is often termed an “expression of opinion” and sometimes known as a “horseback appraisal.”